1. Field of the Invention
The present invention relates to an electromagnetic field analysis performed by Finite Difference Time Domain method.
2. Description of the Background Art
As a simulation method of an electromagnetic wave radiated from an electronic device, various schemes have been suggested in Document 1 (Toru UNO, Finite Difference Time Domain Method for Electromagnetic Field and Antennas, 1st ed., CORONA PUBLISHING CO., LTD., 1998).
For example, one of the schemes of the electromagnetic field analysis is Finite Difference Time Domain method (hereinafter, referred to as FDTD). In the FDTD method, an analysis domain is divided by grid (into cells) to arrange an unknown electromagnetic field in a grid point.
FIG. 36 is a diagram showing a cell structure of the FDTD method. As shown in FIG. 36, in the FDTD method, an analysis is performed with a structure referred to as Yee grid that displaces a grid for arranging an unknown electric field E and a grid for arranging an unknown magnetic field H by half a width of the grids. The FDTD method is an analysis scheme in which a relational expression describing interaction between these unknown electric and magnetic fields and the adjacent unknown electric and magnetic fields is derived by differentiating Maxwell's electromagnetic field analysis equation, based on which the unknown electric and magnetic fields are modified on a certain time-step basis, whereby the entire electromagnetic field behavior is obtained. According to this analysis scheme, the electric field and the magnetic field can be obtained alternately by repeating the procedures of modifying the electric field at a certain time step, modifying the magnetic field after ½ time steps, and modifying the electric field after one time step. However, a step size of the time step needs to satisfy a Courant stability condition with respect to a size of the cell.
Thus, the FDTD method is an analysis method in which by selecting and modeling a cell size in accordance with the fineness of a structure indicating the size of the cell at least necessary for precisely representing a shape of the structure included in an analysis space, and the precision necessary for a required electromagnetic field analysis, the analysis can be applied whatever structure is included inside of the analysis space. However, in the case where an extremely fine structure is included in part of the analysis space as compared with the other parts, if an analysis model is generated using enough small cell to represent the fine structure for all the analysis domain, a differential modifying equation between extremely many electromagnetic field variables will be analyzed using an extremely small time step. This makes calculation resource necessary for the analysis extremely large, and analysis time extremely long.
In contrast, in a sub-grid method introduced in Document 1, the analysis domain is divided, and modeled using different cell sizes. In a boundary section, interpolation is used for connection, and calculation is simultaneously proceeded with while transmitting bi-directional influence to thereby perform the electromagnetic field analysis efficiently. However, since around the boundary section, the analysis becomes unstable, there is a problem in that it is difficult to stably perform the analysis for a long time.
Consequently, in an FDTD-MAS (Finite Difference Time Domain with Multiple-Analysis-Space) method suggested in Japanese Patent Laying-Open No. 2004-038774, a closed surface (hereinafter, referred to as “conversion surface”) surrounding a portion that includes a fine structure and serves as a radiation source, in the entire analysis domain, is considered. In this case, the conversion surface inside is an internal analysis space (hereinafter, referred to as “IAS (Internal Analysis Space)”), and a portion filled with a uniform medium including the IAS is an external analysis space (hereinafter, referred to as “EAS (External Analysis Space)”). For IAS, a small cell is used for modeling, and for EAS, a large cell is used for modeling.
In the FDTD-MAS method, first, for the IAS portion, an analysis is performed on the assumption that a uniform medium similar to that of EAS is filled circumferentially as a boundary condition, and a radiated electromagnetic field on the conversion surface of IAS is stored. Subsequently, the EAS portion is analyzed with the stored radiated electromagnetic field on the conversion surface as a wave source. The calculation of EAS is performed independently from the calculation of IAS, which allows stable analysis to be executed for a long time.
However, in the FDTD-MAS method suggested in Japanese Patent Laying-Open No. 2004-038774, in EAS other than IAS, the analysis cannot be performed with an additional structure or an additional wave source placed besides the uniform medium. This is because in the analysis of IAS, the calculation is executed on the assumption that no wave source exists outside of IAS, and that it is filled with the uniform medium similar to that of the EAS. That is, if an additional structure or an additional wave source is placed at the time of EAS calculation, the influence of scattering in the additional structure portion or the external wave source on EAS causes a different electromagnetic wave from that of the assumption to reach the conversion surface. Since the conversion surface in the FDTD-MAS method behaves as a complete reflector with respect to an electromagnetic wave component different from that of the assumption at the time of IAS calculation, the theoretically proper analysis cannot be performed.
Therefore, although the FDTD-MAS method can be applied to the analysis of the antenna radiation and the like, it is difficult to apply the same to general electromagnetic field analysis. For example, it cannot be applied in a case where in a precision instrument, a detailed analysis is performed with a substrate assumed to a radiative source, and further an electromagnetic field distribution generated outside is found by an analysis with a housing or the like arranged thereoutside as a scattering body, and so on.